Subgroups — #26242809

Order 12032.

732 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#13094012	C₂	1	1	yes	maximal, characteristic
2	#20244326	C₂	1	2	yes	maximal, complemented
3	#20244002	C₂	1	2	yes	maximal, complemented
4	#20244000	C₂	1	2	yes	maximal, complemented
5	#20243684	C₂	1	2	yes	maximal
6	#20243572	C₂	1	2	yes	maximal, complemented
7	#20243569	C₂	1	2	yes	maximal, complemented
8	#20243505	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×#1831	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#10625324	C₂²	1	2	yes	—
11	C₂×#13094012	C₄	1	1	yes	characteristic
12	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
16	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
17	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	2	yes	—
18	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	2	yes	—
19	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	2	yes	—
20	C₂×#13093934	C₂²	1	2	yes	—
21	#15689029	C₄	1	1	yes	characteristic
22	#15689025	C₄	1	1	yes	characteristic
23	#15689014	C₄	1	2	yes	—
24	#15689014	C₄	1	2	yes	—
25	#15688989	C₄	1	1	yes	characteristic
26	C₄×(C₂×D₄₇)⋊C₄	C₂²	1	2	yes	—
27	C₄×(C₂×D₄₇)⋊C₄	C₂²	1	2	yes	—
28	#15688878	C₂²	1	2	yes	—
29	#15688878	C₂²	1	2	yes	—
30	#15688877	C₂²	1	2	yes	—
31	#15688877	C₂²	1	2	yes	—
32	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
34	C₄³×C₄₇	C₂²	1	1	yes	characteristic
35	C₄₇×#336	C₂²	1	2	yes	—
36	C₄₇×#336	C₂²	1	2	yes	—
37	C₂²×Dic₉₄	C₂×C₄	1	1	yes	characteristic
38	C₂²×D₁₈₈	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₄×D₄₇	C₂³	1	2	yes	—
40	C₂×#10625324	—	4	2	no	—
41	C₂×#10625324	—	4	2	no	—
42	C₂×#10625324	—	4	2	no	—
43	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
44	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
45	#13094012	—	2	4	no	—
46	C₄×Dic₉₄	—	4	1	no	—
47	C₄×Dic₉₄	—	4	1	no	—
48	C₄×D₁₈₈	—	4	1	no	—
49	C₄×D₁₈₈	—	4	1	no	—
50	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
52	C₂×Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
53	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
54	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
55	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
56	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
57	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
58	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
59	C₄⋊(C₄₇⋊C₈)	—	4	1	no	—
60	C₄⋊(C₄₇⋊C₈)	—	4	1	no	—
61	Dic₄₇⋊C₈	—	4	2	no	—
62	(C₂×D₄₇)⋊C₈	—	4	2	no	—
63	(C₂×D₄₇)⋊C₈	—	4	2	no	—
64	(C₂×D₄₇)⋊C₈	—	4	2	no	—
65	#13093934	—	4	2	no	—
66	C₄₇⋊#95	C₂×C₄	1	2	yes	—
67	C₄₇⋊#95	C₂×C₄	1	2	yes	—
68	C₄₇⋊#95	C₂×C₄	1	2	yes	—
69	C₄₇⋊#95	C₂×C₄	1	2	yes	—
70	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
71	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
72	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
79	C₄⋊C₈×C₄₇	—	4	1	no	—
80	C₄⋊C₈×C₄₇	—	4	1	no	—
81	C₂³×D₄₇	C₂²×C₄	1	2	yes	—
82	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
89	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
90	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
91	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
92	C₂×D₁₈₈	—	2	2	no	—
93	C₂×D₁₈₈	—	4	1	no	—
94	C₂×D₁₈₈	—	4	1	no	—
95	C₂×C₄×D₄₇	—	2	2	no	—
96	C₂×C₄×D₄₇	—	2	2	no	—
97	C₂×C₄×D₄₇	—	2	2	no	—
98	C₂×C₄×D₄₇	—	2	2	no	—
99	C₂×C₄×D₄₇	—	2	2	no	—
100	C₂×C₄×D₄₇	—	2	2	no	—
101	C₂×Dic₉₄	—	2	2	no	—
102	C₂×Dic₉₄	—	4	1	no	—
103	C₂×Dic₉₄	—	4	1	no	—
104	C₂×C₈×C₄₇	—	2	2	no	—
105	C₂×C₈×C₄₇	—	2	2	no	—
106	C₂×C₈×C₄₇	—	2	2	no	—
107	C₂×C₈×C₄₇	—	2	2	no	—
108	C₂×C₈×C₄₇	—	2	2	no	—
109	C₂×C₈×C₄₇	—	2	2	no	—
110	C₄²×C₄₇	—	2	1	no	—
111	C₄²×C₄₇	—	2	1	no	—
112	C₄²×C₄₇	—	2	1	no	—
113	C₄²×C₄₇	—	2	1	no	—
114	C₄²×C₄₇	—	2	1	no	—
115	C₄²×C₄₇	—	2	1	no	—
116	C₄²×C₄₇	—	4	1	no	—
117	C₄²×C₄₇	—	4	1	no	—
118	C₄²×C₄₇	—	4	1	no	—
119	C₄²×C₄₇	M₁₆	1	4	yes	complemented
120	(C₂×D₄₇)⋊C₄	—	2	4	no	—
121	(C₂×D₄₇)⋊C₄	—	2	4	no	—
122	(C₂×D₄₇)⋊C₄	—	4	2	no	—
123	(C₂×D₄₇)⋊C₄	—	4	2	no	—
124	(C₂×D₄₇)⋊C₄	—	4	2	no	—
125	C₄⋊Dic₄₇	—	4	1	no	—
126	C₄⋊Dic₄₇	—	4	1	no	—
127	Dic₄₇⋊C₄	—	4	2	no	—
128	C₄×Dic₄₇	—	2	2	no	—
129	C₄×Dic₄₇	—	2	2	no	—
130	C₂×C₄₇⋊C₈	—	2	2	no	—
131	C₂×C₄₇⋊C₈	—	2	2	no	—
132	C₂×C₄₇⋊C₈	—	2	2	no	—
133	C₂×C₄₇⋊C₈	—	2	2	no	—
134	C₂×C₄₇⋊C₈	—	2	2	no	—
135	C₂×C₄₇⋊C₈	—	2	2	no	—
136	#10625324	—	4	8	no	—
137	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
138	C₂²×D₄₇	—	2	2	no	—
139	C₂²×D₄₇	—	2	2	no	—
140	C₂²×D₄₇	—	2	2	no	—
141	C₂²×D₄₇	—	2	2	no	—
142	C₂²×D₄₇	—	2	2	no	—
143	C₂²×D₄₇	—	2	2	no	—
144	C₂²×D₄₇	—	2	2	no	—
145	C₂×C₄×C₄₇	—	2	1	no	—
146	C₂×C₄×C₄₇	—	2	1	no	—
147	C₂×C₄×C₄₇	—	2	1	no	—
148	C₂×C₄×C₄₇	—	2	1	no	—
149	C₂×C₄×C₄₇	—	2	1	no	—
150	C₂×C₄×C₄₇	—	2	1	no	—
151	C₂×C₄×C₄₇	—	2	1	no	—
152	C₂×C₄×C₄₇	—	2	1	no	—
153	C₂×C₄×C₄₇	—	2	1	no	—
154	C₂×C₄×C₄₇	—	2	1	no	—
155	C₂×C₄×C₄₇	—	2	1	no	—
156	C₂×C₄×C₄₇	—	2	1	no	—
157	C₂×C₄×C₄₇	—	2	1	no	—
158	C₂×C₄×C₄₇	—	2	1	no	—
159	C₂×C₄×C₄₇	—	2	1	no	—
160	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
161	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
162	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
163	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
164	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
165	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
166	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
167	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
168	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
169	C₂×Dic₄₇	—	2	2	no	—
170	C₂×Dic₄₇	—	2	2	no	—
171	C₂×Dic₄₇	—	2	2	no	—
172	C₂×Dic₄₇	—	2	2	no	—
173	C₂×Dic₄₇	—	2	2	no	—
174	C₂×Dic₄₇	—	2	2	no	—
175	C₂×Dic₄₇	—	2	2	no	—
176	C₂×Dic₄₇	—	2	2	no	—
177	C₂×Dic₄₇	—	2	2	no	—
178	D₁₈₈	—	4	4	no	—
179	C₄×D₄₇	—	4	2	no	—
180	C₄×D₄₇	—	4	2	no	—
181	C₄×D₄₇	—	4	2	no	—
182	C₄×D₄₇	—	4	2	no	—
183	Dic₉₄	—	4	4	no	—
184	C₈×C₄₇	—	4	2	no	—
185	C₈×C₄₇	—	4	2	no	—
186	C₄₇⋊C₈	—	4	2	no	—
187	C₄₇⋊C₈	—	4	2	no	—
188	#23353	—	47	1	no	maximal, Sylow
189	C₂²×C₄₇	#518	1	1	yes	characteristic
190	C₂²×C₄₇	#520	1	1	yes	characteristic
191	C₂²×C₄₇	#520	1	1	yes	characteristic
192	C₂²×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
193	C₂²×C₄₇	#568	1	1	yes	characteristic
194	C₂²×C₄₇	#568	1	1	yes	characteristic
195	C₂²×C₄₇	#568	1	1	yes	characteristic
196	C₂×D₄₇	—	4	2	no	—
197	C₂×D₄₇	—	4	2	no	—
198	C₂×D₄₇	—	4	2	no	—
199	C₂×D₄₇	—	4	2	no	—
200	C₂×D₄₇	—	4	2	no	—
201	C₂×D₄₇	—	4	2	no	—
202	C₂×D₄₇	—	4	2	no	—
203	C₄×C₄₇	—	2	2	no	—
204	C₄×C₄₇	—	2	2	no	—
205	C₄×C₄₇	—	2	2	no	—
206	C₄×C₄₇	—	4	1	no	—
207	C₄×C₄₇	—	4	1	no	—
208	C₄×C₄₇	—	4	1	no	—
209	C₄×C₄₇	H(3,𝔽₄)	1	1	yes	characteristic
210	C₄×C₄₇	#562	1	1	yes	characteristic
211	C₄×C₄₇	#562	1	1	yes	characteristic
212	C₄×C₄₇	#563	1	1	yes	characteristic
213	Dic₄₇	—	4	2	no	—
214	Dic₄₇	—	4	2	no	—
215	Dic₄₇	—	4	2	no	—
216	C₄×#124	—	47	1	no	—
217	#1985	—	47	2	no	—
218	#1924	—	47	2	no	—
219	#1924	—	47	2	no	—
220	#1870	—	47	2	no	—
221	#1851	—	47	2	no	—
222	#1851	—	47	2	no	—
223	#1831	—	47	1	no	—
224	#1831	D₄₇	1	1	yes	characteristic, complemented
225	C₂×C₄₇	#2379	1	1	yes	characteristic
226	C₂×C₄₇	#2975	1	1	yes	characteristic
227	C₂×C₄₇	#2980	1	1	yes	characteristic
228	C₂×C₄₇	#2989	1	1	yes	characteristic
229	C₂×C₄₇	#2989	1	1	yes	characteristic
230	C₂×C₄₇	#2995	1	1	yes	characteristic
231	C₂×C₄₇	#2995	1	1	yes	characteristic
232	D₄₇	—	8	2	no	—
233	C₂²×M₁₆	—	47	2	no	—
234	C₂×#124	—	47	1	no	—
235	C₂×C₄×Q₈	—	47	1	no	—
236	C₂×C₄×D₄	—	47	1	no	—
237	C₂×C₄⋊C₈	—	47	2	no	—
238	C₂×C₄⋊C₈	—	47	1	no	—
239	C₂×C₄⋊C₈	—	47	1	no	—
240	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
241	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
242	C₂×C₂²⋊C₈	—	47	2	no	—
243	C₂×C₂²⋊C₈	—	47	2	no	—
244	C₂×C₂²⋊C₈	—	47	2	no	—
245	C₂×#97	—	47	2	no	—
246	#391	—	47	1	no	—
247	#390	—	47	1	no	—
248	#388	—	47	2	no	—
249	#388	—	47	2	no	—
250	#382	—	47	1	no	—
251	C₄×C₂²⋊C₄	—	47	2	no	—
252	C₄×C₂²⋊C₄	—	47	2	no	—
253	C₄³	C₂×D₄₇	1	1	yes	characteristic
254	#336	—	47	2	no	—
255	#336	—	47	2	no	—
256	#336	—	47	2	no	—
257	#336	—	47	2	no	—
258	#336	C₂×D₄₇	1	2	yes	—
259	#336	C₂×D₄₇	1	2	yes	—
260	C₄₇	#23353	1	1	yes	characteristic, complemented, Sylow
261	C₂²×Q₈	—	47	1	no	—
262	C₂²×D₄	—	47	1	no	—
263	C₂³×C₄	—	47	2	no	—
264	C₂×M₁₆	—	188	2	no	—
265	C₂×M₁₆	—	188	2	no	—
266	C₂×M₁₆	—	188	2	no	—
267	C₂²×C₈	—	47	2	no	—
268	C₂²×C₈	—	47	2	no	—
269	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
270	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
271	#124	—	94	4	no	—
272	C₄×Q₈	—	188	1	no	—
273	C₄×Q₈	—	188	1	no	—
274	C₄×D₄	—	188	1	no	—
275	C₄×D₄	—	188	1	no	—
276	C₂×C₄⋊C₄	—	47	1	no	—
277	C₂×C₄⋊C₄	—	47	2	no	—
278	C₂×C₄⋊C₄	—	47	1	no	—
279	C₂×C₂²⋊C₄	—	47	2	no	—
280	C₂×C₂²⋊C₄	—	47	2	no	—
281	C₂×C₂²⋊C₄	—	47	2	no	—
282	C₂×C₂²⋊C₄	—	47	2	no	—
283	C₂×C₂²⋊C₄	—	47	2	no	—
284	C₂×C₄²	—	47	2	no	—
285	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
286	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
287	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
288	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
289	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
290	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
291	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
292	C₄⋊C₈	—	4	1	no	—
293	C₄⋊C₈	—	4	1	no	—
294	C₄⋊C₈	—	188	1	no	—
295	C₄⋊C₈	—	188	1	no	—
296	C₄⋊C₈	—	188	2	no	—
297	C₂²⋊C₈	—	188	2	no	—
298	C₂²⋊C₈	—	188	2	no	—
299	C₂²⋊C₈	—	188	2	no	—
300	#97	—	188	2	no	—
301	#95	—	47	2	no	—
302	#95	—	47	2	no	—
303	#95	—	47	2	no	—
304	#95	—	47	2	no	—
305	C₂⁴	—	47	2	no	—
306	C₂×Q₈	—	94	2	no	—
307	C₂×Q₈	—	188	1	no	—
308	C₂×Q₈	—	188	1	no	—
309	C₂×D₄	—	94	2	no	—
310	C₂×D₄	—	188	1	no	—
311	C₂×D₄	—	188	1	no	—
312	C₂²×C₄	—	47	2	no	—
313	C₂²×C₄	—	47	2	no	—
314	C₂²×C₄	—	47	2	no	—
315	C₂²×C₄	—	94	2	no	—
316	C₂²×C₄	—	94	2	no	—
317	C₂²×C₄	—	94	2	no	—
318	C₂²×C₄	—	94	2	no	—
319	C₂²×C₄	—	94	2	no	—
320	C₂²×C₄	—	94	2	no	—
321	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
322	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
323	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
324	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
325	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
326	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
327	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
328	M₁₆	—	188	8	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	94	2	no	—
336	C₂×C₈	—	94	2	no	—
337	C₂×C₈	—	94	2	no	—
338	C₂×C₈	—	94	2	no	—
339	C₂×C₈	—	94	2	no	—
340	C₂×C₈	—	94	2	no	—
341	C₄⋊C₄	—	188	2	no	—
342	C₄⋊C₄	—	188	1	no	—
343	C₄⋊C₄	—	188	1	no	—
344	C₂²⋊C₄	—	94	4	no	—
345	C₂²⋊C₄	—	94	4	no	—
346	C₂²⋊C₄	—	188	2	no	—
347	C₂²⋊C₄	—	188	2	no	—
348	C₂²⋊C₄	—	188	2	no	—
349	C₄²	—	2	1	no	—
350	C₄²	—	2	1	no	—
351	C₄²	—	2	1	no	—
352	C₄²	—	2	1	no	—
353	C₄²	—	2	1	no	—
354	C₄²	—	2	1	no	—
355	C₄²	—	4	1	no	—
356	C₄²	—	4	1	no	—
357	C₄²	—	4	1	no	—
358	C₄²	—	94	2	no	—
359	C₄²	—	94	2	no	—
360	C₄²	#10625324	1	4	yes	complemented
361	C₂³	—	94	2	no	—
362	C₂³	—	94	2	no	—
363	C₂³	—	94	2	no	—
364	C₂³	—	94	2	no	—
365	C₂³	—	94	2	no	—
366	C₂³	—	94	2	no	—
367	C₂³	—	94	2	no	—
368	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
369	Q₈	—	188	4	no	—
370	D₄	—	188	4	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	94	2	no	—
387	C₂×C₄	—	94	2	no	—
388	C₂×C₄	—	94	2	no	—
389	C₂×C₄	—	94	2	no	—
390	C₂×C₄	—	94	2	no	—
391	C₂×C₄	—	94	2	no	—
392	C₂×C₄	—	94	2	no	—
393	C₂×C₄	—	94	2	no	—
394	C₂×C₄	—	94	2	no	—
395	C₂×C₄	—	188	2	no	—
396	C₂×C₄	—	188	2	no	—
397	C₂×C₄	—	188	2	no	—
398	C₂×C₄	—	188	2	no	—
399	C₂×C₄	C₂×#10625324	1	2	yes	—
400	C₂×C₄	C₂×#10625324	1	2	yes	—
401	C₂×C₄	C₂×#10625324	1	2	yes	—
402	C₂×C₄	#13094069	1	1	yes	characteristic
403	C₂×C₄	#13094070	1	1	yes	characteristic
404	C₂×C₄	#13094070	1	1	yes	characteristic
405	C₂×C₄	#13094070	1	1	yes	characteristic
406	C₂×C₄	#13094071	1	1	yes	characteristic
407	C₂×C₄	#13094072	1	1	yes	characteristic
408	C₈	—	4	2	no	—
409	C₈	—	4	2	no	—
410	C₈	—	188	2	no	—
411	C₈	—	188	2	no	—
412	C₂²	—	188	2	no	—
413	C₂²	—	188	2	no	—
414	C₂²	—	188	2	no	—
415	C₂²	—	188	2	no	—
416	C₂²	—	188	2	no	—
417	C₂²	—	188	2	no	—
418	C₂²	—	188	2	no	—
419	C₂²	#15689597	1	1	yes	characteristic
420	C₂²	#15689603	1	1	yes	characteristic
421	C₂²	#15689604	1	1	yes	characteristic
422	C₂²	C₂²×#10625324	1	1	yes	characteristic
423	C₂²	#15689889	1	1	yes	characteristic
424	C₂²	#15689889	1	1	yes	characteristic
425	C₂²	#15689889	1	1	yes	characteristic
426	C₄	—	2	2	no	—
427	C₄	—	2	2	no	—
428	C₄	—	2	2	no	—
429	C₄	—	4	1	no	—
430	C₄	—	4	1	no	—
431	C₄	—	4	1	no	—
432	C₄	—	188	2	no	—
433	C₄	—	188	2	no	—
434	C₄	—	188	2	no	—
435	C₄	#15689865	1	1	yes	characteristic
436	C₄	#15689867	1	1	yes	characteristic
437	C₄	#15689871	1	1	yes	characteristic
438	C₄	#15689877	1	1	yes	characteristic
439	C₂	—	376	2	no	—
440	C₂	#20246559	1	1	yes	characteristic
441	C₂	#20252428	1	1	yes	characteristic
442	C₂	#20252458	1	1	yes	characteristic
443	C₂	#20252501	1	1	yes	characteristic
444	C₂	#20252506	1	1	yes	characteristic
445	C₂	#20252555	1	1	yes	characteristic
446	C₂	#20252560	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂³×C₄
Fitting	C₄₇×#1831	C₂
prime radical	C₂²×D₁₈₈	C₂×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1831	D₄₇
hypocenter	C₄₇	#23353
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #1831

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. #20244326	C₂	semidirect
3. #20244002	C₂	semidirect
4. #20244000	C₂	semidirect
6. #20243572	C₂	semidirect
7. #20243569	C₂	semidirect
8. #20243505	C₂	semidirect
9. C₄₇×#1831	C₂	semidirect
119. C₄²×C₄₇	M₁₆	semidirect
224. #1831	D₄₇	semidirect
260. C₄₇	#23353	semidirect
360. C₄²	#10625324	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₄×#13094012	2
#20244326	2
#20244002	2
#20244000	2
#20243684	2
#20243572	2
#20243569	2
#20243505	2
C₄₇×#1831	2
#23353	47